We compared the empirically observed values – of the maximum correlation reached and the time at which the largest magnitude correlation occurred – to those expected under two null models: (i) a topological null model that preserved only the number of edges and their total strength, and (ii) a spatially embedded null model that also preserved the relationship between edge strength and edge distance. Instantiations of the topological null model were generated using the Brain Connectivity Toolbox [1]}. The rewiring algorithm begins by randomly choosing two pairs of edges (\(i \rightarrow j\)  and \(k \rightarrow l\) ) and continues by swapping their origin and termination points (\(i \rightarrow k\)  and \(j \rightarrow l\) ). Here, we performed \(2 \times 10^{4}\)  bidirectional edge swaps per network. Instantiations of the spatially embedded model were generated using code from [2]}. The rewiring algorithm begins by calculating the Euclidean distance between the average coordinates of all regions in the Lausanne atlas, and continues by removing the effect of distance on the mean and variance of the edge weights, randomly rewiring, and then adding the effect of distance back to the newly rewired graph. For both topological and spatial null model analyses, a new random graph was generated for every trial (minimum number of trials was 192). Null models were created from the stabilized rather than raw versions of the structural matrices, and – in the optimal control analyses – were also scaled by a parameter \(\gamma \)  to reduce the error of the calculation (see Supplemental Materials).
